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The NEMO-3 experiment at the Modane Underground Laboratory has investigatedthe double-$\beta$ decay of $^{48}{\rm Ca}$. Using $5.25$ yr of data recordedwith a $6.99\,{\rm g}$ sample of $^{48}{\rm Ca}$, approximately $150$double-$\beta$ decay candidate events have been selected with asignal-to-background ratio greater than $3$. The half-life for the two-neutrinodouble-$\beta$ decay of $^{48}{\rm Ca}$ has been measured to be$T^{2\nu}_{1/2}\,=\,[6.4\, ^{+0.7}_{-0.6}{\rm (stat.)} \, ^{+1.2}_{-0.9}{\rm(syst.)}] \times 10^{19}\,{\rm yr}$. A search for neutrinoless double-$\beta$decay of $^{48}{\rm Ca}$ yields a null result and a corresponding lower limiton the half-life is found to be $T^{0\nu}_{1/2} > 2.0 \times 10^{22}\,{\rm yr}$at $90\%$ confidence level, translating into an upper limit on the effectiveMajorana neutrino mass of $< m_{\beta\beta} > < 6.0 - 26$ ${\rm eV}$, with therange reflecting different nuclear matrix element calculations. Limits are alsoset on models involving Majoron emission and right-handed currents.

Measurement of the double-beta decay half-life and search for the neutrinoless double-beta decay of $^{48}{\rm Ca}$ with the NEMO-3 detector